All Questions
5 questions
7
votes
2
answers
2k
views
Are algebraic geometry error correcting codes (Goppa codes) "good" ?
Question (informal version): Are algebraic geometry error correcting codes (V.D. Goppa codes) "good" ?
Some details. There is certain construction of error-correcting codes by means of algebraic ...
- 24.9k
4
votes
1
answer
196
views
Polynomial time decodable binary linear codes achieving $GV$ bound?
Are there explicit or random construction of linear codes that achieve the $GV$ bound with polynomial time decodable property with alphabet size $q=2$?
Tsfasman, Manin, Vladut beat the bound at ...
- 13.9k
3
votes
1
answer
531
views
How many vectors of Hamming weight L in "random" K dimensional subspace of F_2^N ? Or how good/bad is random linear block code ?
Consider linear $N$-dimensional space $F_2^N$.
Consider its $K$ dimensional subspace $V \subset F_2^N$.
Let us calculate $w(k,V,N)$ number of vectors in $V$ of Hamming weight $k$ in $V$.
Since there ...
- 24.9k
2
votes
0
answers
142
views
List decodability of Reed-Solomon codes beyond the Johnson bound
In a paper on a proximity test for Reed-Solomon codes the authors state an "extremely optimistical" conjecture on the list decodability of Reed-Solomon codes (over prime fields $\mathbb F_q$)...
- 81
0
votes
1
answer
262
views
Number of points on a complex sphere with pairwise inner product restriction
Considered the following inner products:
$(1)$ $\langle x,y \rangle = \sum_{t=1}^{n}x_{t}y_{t}$
$(2)$ $\langle x,y \rangle_{c} = \sum_{t=1}^{n}x_{t}\bar{y}_{t}$
consider the following surfaces:
$\...
- 13.9k